Alessio Figalli won the most important mathematics prize in the world, the Fields Medal, in 2018. This put him in the spotlight and made hima role model, especially for the next generation: matriculation figures for mathematics in his native Italy surged.

Fields Medal Winner 2018: Alessio Figalli (Photos: Basil Stücheli/ETH Board)

Alessio Figalli hurries into his office in the main building of ETH Zurich and apologises in a heartfelt Italian way for being two minutes late. His shirt freshly ironed; on his desk a few piles of papers, which he quickly straightens up. The autumn sun shines in, he pulls the blinds and apologises for the mess, which is hardly worth mentioning – ticking the boxes for “light-shy” and “likes things to be tidy”. Otherwise, however, Figalli does not strike you as being eccentric. He comes across as the sort of sociable young man you would trust with your financial affairs. In fact, he couldn’t be any less like the stereotype of a mathematician. And that stereotype actually gets on Figalli’s nerves. “Why do we believe that mathematicians always have to be a little unworldly or quirky?” Most of them don’t fit that image. He first decided to go to a grammar school specialising in humanities, including Greek and Latin, before being drawn to the legendary Scuola Normale Superiore in Pisa via the Mathematics Olympiad.

Alessio Figalli, professor of mathematics

The office still fits the cliché, however with the stereotypical board, scribbled all over with formulas and diagrams. Yes, sometimes he likes to get stuck into his work on there. It can be rather liberating to wipe the board clean and rearrange your thoughts. Figalli says, however, that he simply works best with a pen and paper – and whenever possible, the computer stays switched off. He sometimes wonders whether the rhythm of today’s society is healthy and whether we should not take it down a few gears. Mathematics, he says, moves along at a rather slow pace. Every single line of thought has to be carefully examined and proven. That takes time.

And what if the computer did some of the work in the background? Figalli’s brow becomes furrowed. He is “anxious” at the prospect that artificial intelligence might soon learn to draw and link logical conclusions. While there is not much to be said against automated systems acquiring this skill in theory, he cannot (or does not want to) imagine that they could also achieve the creative ability to do so. And he refers to chess; all the fun has gone by the wayside since the best computers can now beat any human player without any bother.

”Mathematics is everywhere. A discipline for modelling the world.”

He chose mathematics because of its logic and order, because it was “clean” and not a matter of faith. However, he chose this field of research precisely be-cause of the “fun” that rich mathematical problems offer. He was awarded the Fields Medal because he was able to demonstrate how questions about the optimum distribution of resources intertwine with the geometry of space. The findings can be applied in economics, probability theory or fluid mechanics. So, is he contributing towards the unstoppable drive to increase efficiency, with the ever-more, ever-faster culture? No, he doesn’t like to see it that way, because efficiency can also enable us to save time to do other things. In essence, however, it is good to know that our discoveries can also be beneficial. “The closer you get to the application, the better.” But he wouldn’t let the application steer him in his work. The mathematics would ultimately have to stand on its own merits. Figalli mentions the Fourier transform. Without that, it is inconceivable that today’s electronics would function, although Fourier could not have foreseen that.

He regards communication among researchers, be they physicists or biologists, as a fundamental stumbling block in linking basic mathematical research to scientific applications: “We just don’t understand one another.” Mediators who are familiar with both fields can help, but the approaches will always re-main essentially different. “There’s still no sound theory for the phenomenon of how planes fly; it’s a very difficult field mathematically.” And it sums up the difference between mathematics and physics neatly. Of course, the absence of any rock-solid evidence does not stop the engineer from building aircraft. Nor does it stop us from boarding them.